Distribution of high-dimensional entanglement via an intra-city free-space link

Experimental realization of a transmissive microwave metasurface for dual vector vortex beams generation

This work presents a theoretical design and experimental demonstration of a transmissive microwave metasurface for generating dual-vector vortex beams (VVBs). The proposed metasurface consists of an array of pixelated dartboard discretization meta-atoms. By rotating the meta-atoms from 0° to 180°, a Pancharatnam-Barry (P-B) phase covering the full 360° range is achieved, with a transmittance exceeding 90% over the frequency range from 9.7 to 10.2 GHz. The measured results demonstrate that when a linearly polarized microwave normally impinges on the metasurface, the transmitted beams correspond to the dual VVBs with different directions. A good agreement among Poincaré sphere theory, full-wave simulation, and experimental measurement is observed. This proposed transmissive microwave metasurface for VVBs may offer promising applications in communications and radar detection.

Practical high-dimensional quantum key distribution protocol over deployed multicore fiber

Quantum key distribution (QKD) is a secure communication scheme for sharing symmetric cryptographic keys based on the laws of quantum physics, and is considered a key player in the realm of cyber-security. A critical challenge for QKD systems comes from the fact that the ever-increasing rates at which digital data are transmitted require more and more performing sources of quantum keys, primarily in terms of secret key generation rate. High-dimensional QKD based on path encoding has been proposed as a candidate approach to address this challenge. However, while proof-of-principle demonstrations based on lab experiments have been reported in the literature, demonstrations in realistic environments are still missing. Here we report the generation of secret keys in a 4-dimensional hybrid time-path-encoded QKD system over a 52-km deployed multicore fiber link forming by looping back two cores of a 26-km 4-core optical fiber. Our results indicate that robust high-dimensional QKD can be implemented in a realistic environment by combining standard telecom equipment with emerging multicore fiber technology.

Generation and characterization of ultrabroadband polarization-frequency hyperentangled photons

We generate ultrabroadband photon pairs entangled in both polarization and frequency bins through an all-waveguided Sagnac source covering the entire optical C- and L-bands (1530-1625 nm). We perform comprehensive characterization of high-fidelity states in multiple dense wavelength-division multiplexed channels, achieving full tomography of effective four-qubit systems. Additionally, leveraging the inherent high dimensionality of frequency encoding and our electro-optic measurement approach, we demonstrate the scalability of our system to higher dimensions, reconstructing states in a 36-dimensional Hilbert space consisting of two polarization qubits and two frequency-bin qutrits. Our findings hold potential significance for quantum networking, particularly dense coding and entanglement distillation in wavelength-multiplexed quantum networks.

Training a quantum measurement device to discriminate unknown non-orthogonal quantum states

Here, we study the problem of decoding information transmitted through unknown quantum states. We assume that Alice encodes an alphabet into a set of orthogonal quantum states, which are then transmitted to Bob. However, the quantum channel that mediates the transmission maps the orthogonal states into non-orthogonal states, possibly mixed. If an accurate model of the channel is unavailable, then the states received by Bob are unknown. In order to decode the transmitted information we propose to train a measurement device to achieve the smallest possible error in the discrimination process. This is achieved by supplementing the quantum channel with a classical one, which allows the transmission of information required for the training, and resorting to a noise-tolerant optimization algorithm. We demonstrate the training method in the case of minimum-error discrimination strategy and show that it achieves error probabilities very close to the optimal one. In particular, in the case of two unknown pure states, our proposal approaches the Helstrom bound. A similar result holds for a larger number of states in higher dimensions. We also show that a reduction of the search space, which is used in the training process, leads to a considerable reduction in the required resources. Finally, we apply our proposal to the case of the phase flip channel reaching an accurate value of the optimal error probability.

Application and Development of QKD-Based Quantum Secure Communication

Quantum key distribution (QKD) protocols have unique advantages of enabling symmetric key sharing with information-theoretic security (ITS) between remote locations, which ensure the long-term security even in the era of quantum computation. QKD-based quantum secure communication (QSC) enhancing the security of key generation and update rate of keys, which could be integrated with a variety of cryptographic applications and communication protocols, has become one of the important solutions to improve information security. In recent years, the research on QKD has been active and productive, the performance of novel protocol systems has been improved significantly, and the feasibility of satellite-based QKD has been experimentally verified. QKD network construction, application exploration, and standardization have been carried out in China as well as other countries and regions around the world. Although QKD-based QSC applications and industrialization are still in the initial stage, the research and exploration momentum is positive and more achievements could be expected in the future.

Longitudinal evolution from scalar to vector beams assembled from all-dielectric metasurfaces

Vector vortex beams (VVBs) with non-uniform polarization states have a wide range of applications, from particle capture to quantum information. Here, we theoretically demonstrate a generic design for all-dielectric metasurfaces operating in the terahertz (THz) band, characterized as a longitudinal evolution from scalar vortices carrying homogeneous polarization states to inhomogeneous vector vortices with polarization singularities. The order of the converted VVBs can be arbitrarily tailored by manipulating the topological charge embedded in two orthogonal circular polarization channels. The introduction of the extended focal length and the initial phase difference effectively guarantees the smoothness of the longitudinal switchable behavior. A generic design approach based on vector-generated metasurfaces can assist in the exploration of new singular properties of THz optical fields.

Propagation-induced revival of entanglement in the angle-OAM bases

Although the continuous-variable position-momentum entanglement of photon pairs produced by parametric down-conversion has applicability in several quantum information applications, it is not suitable for applications involving long-distance propagation. This is because entanglement in the position-momentum bases, as seen through Einstein-Podolsky-Rosen (EPR)-correlation measurements, decays very rapidly with photons propagating away from the source. In contrast, in this article, we show that in the continuous-variable bases of angle-orbital angular momentum (OAM), the entanglement, as seen through EPR-correlation measurements, exhibits a remarkably different behavior. As with the position-momentum bases, initially, the entanglement in the angle-OAM bases also decays with propagation, and after a few centimeters of propagation, there is no angle-OAM entanglement left. However, as the photons continue to travel further away from the source, the entanglement in the angle-OAM bases revives. We theoretically and experimentally demonstrate this behavior and show that angle-OAM entanglement revives even in the presence of strong turbulence.

Design of Metasurface with Nanoslits on Elliptical Curves for Generation of Dual-Channel Vector Beams

The manipulations of nanoscale multi-channel vector beams (VBs) by metasurfaces hold potential applications in various important fields. In this paper, the metasurface with two sets of nanoslits arranged on elliptic curves was proposed to generate the dual-channel focused vector beams (FVBs). Each set of nanoslits was composed of the in-phase and the out-of-phase groups of nanoslits to introduce the constructive interference and destructive interference of the output light field of the nanoslits, focusing the converted spin component and eliminating the incident spin component at the focal point. The two sets of nanoslits for the channels at the two focal points were interleaved on the same ellipses, and by setting their parameters independently, the FVBs in the two channels are generated under illumination of linearly polarized light, while their orders and polarization states of FVBs were controlled independently. The generation of the FVBs with the designed metasurfaces was demonstrated by the finite-difference time domain (FDTD) simulations and by the experimental verifications. The work in this paper is of great significance for the generation of miniaturized multi-channel VBs and for broadening the applications of metasurfaces.

Measuring dimensionality and purity of high-dimensional entangled states

High-dimensional entangled states are promising candidates for increasing the security and encoding capacity of quantum systems. While it is possible to witness and set bounds for the entanglement, precisely quantifying the dimensionality and purity in a fast and accurate manner remains an open challenge. Here, we report an approach that simultaneously returns the dimensionality and purity of high-dimensional entangled states by simple projective measurements. We show that the outcome of a conditional measurement returns a visibility that scales monotonically with state dimensionality and purity, allowing for quantitative measurements for general photonic quantum systems. We illustrate our method using two separate bases, the orbital angular momentum and pixels bases, and quantify the state dimensionality by a variety of definitions over a wide range of noise levels, highlighting its usefulness in practical situations. Importantly, the number of measurements needed in our approach scale linearly with dimensions, reducing data acquisition time significantly. Our technique provides a simple, fast and direct measurement approach.

Experimental Single-Copy Entanglement Distillation

The phenomenon of entanglement marks one of the furthest departures from classical physics and is indispensable for quantum information processing. Despite its fundamental importance, the distribution of entanglement over long distances through photons is unfortunately hindered by unavoidable decoherence effects. Entanglement distillation is a means of restoring the quality of such diluted entanglement by concentrating it into a pair of qubits. Conventionally, this would be done by distributing multiple photon pairs and distilling the entanglement into a single pair. Here, we turn around this paradigm by utilizing pairs of single photons entangled in multiple degrees of freedom. Specifically, we make use of the polarization and the energy-time domain of photons, both of which are extensively field tested. We experimentally chart the domain of distillable states and achieve relative fidelity gains up to 13.8%. Compared to the two-copy scheme, the distillation rate of our single-copy scheme is several orders of magnitude higher, paving the way towards high-capacity and noise-resilient quantum networks.

Compound Vector Light Generator Based on a Metasurface

In view of wide applications of vector light with a non-uniform polarization state, a compound vector light generator is proposed to generate compound vector light. One compound vector light contains two or more non-uniform polarization modes and several annular intensities, which can carry more polarization information and possess higher dimensional singularity. The proposed compound vector light generator consists of cross nanoholes with high polarization conversion efficiency; it works under linear polarized light, and the mode of the generated compound vector light can be adjusted through rotating cross nanoholes. The structure parameters of the compound vector light generator are optimized with the aid of numerical simulation, and the simulation results for the generated light fields verify the performance of the proposed device. The advancement of the compound vector light and metasurface design of the compound vector light generator can assist in the exploration of novel singular properties of light fields and the broadening of applications of vector light fields.

Procedure via cross-Kerr nonlinearities for encoding single logical qubit information onto four-photon decoherence-free states

We propose a photonic procedure using cross-Kerr nonlinearities (XKNLs) to encode single logical qubit information onto four-photon decoherence-free states. In quantum information processing, a decoherence-free subspace can secure quantum information against collective decoherence. Therefore, we design a procedure employing nonlinear optical gates, which are composed of XKNLs, quantum bus beams, and photon-number-resolving measurements with linear optical devices, to conserve quantum information by encoding quantum information onto four-photon decoherence-free states (single logical qubit information). Based on our analysis in quantifying the affection (photon loss and dephasing) of the decoherence effect, we demonstrate the experimental condition to acquire the reliable procedure of single logical qubit information having the robustness against the decoherence effect.

Creating heralded hyper-entangled photons using Rydberg atoms

Entangled photon pairs are a fundamental component for testing the foundations of quantum mechanics, and for modern quantum technologies such as teleportation and secured communication. Current state-of-the-art sources are based on nonlinear processes that are limited in their efficiency and wavelength tunability. This motivates the exploration of physical mechanisms for entangled photon generation, with a special interest in mechanisms that can be heralded, preferably at telecommunications wavelengths. Here we present a mechanism for the generation of heralded entangled photons from Rydberg atom cavity quantum electrodynamics (cavity QED). We propose a scheme to demonstrate the mechanism and quantify its expected performance. The heralding of the process enables non-destructive detection of the photon pairs. The entangled photons are produced by exciting a rubidium atom to a Rydberg state, from where the atom decays via two-photon emission (TPE). A Rydberg blockade helps to excite a single Rydberg excitation while the input light field is more efficiently collectively absorbed by all the atoms. The TPE rate is significantly enhanced by a designed photonic cavity, whose many resonances also translate into high-dimensional entanglement. The resulting high-dimensionally entangled photons are entangled in more than one degree of freedom: in all of their spectral components, in addition to the polarization-forming a hyper-entangled state, which is particularly interesting in high information capacity quantum communication. We characterize the photon comb states by analyzing the Hong-Ou-Mandel interference and propose proof-of-concept experiments.

Entangled photon-pair sources based on three-wave mixing in bulk crystals

Entangled photon pairs are a critical resource in quantum communication protocols ranging from quantum key distribution to teleportation. The current workhorse technique for producing photon pairs is via spontaneous parametric down conversion (SPDC) in bulk nonlinear crystals. The increased prominence of quantum networks has led to a growing interest in deployable high performance entangled photon-pair sources. This manuscript provides a review of the state-of-the-art bulk-optics-based SPDC sources with continuous wave pump and discusses some of the main considerations when building for deployment.

Dissipative preparation of qutrit entanglement via periodically modulated Rydberg double antiblockade

We propose a mechanism of Rydberg double antiblockade by virtue of a resonant dipole-dipole interaction between a pair of Rydberg atoms placed at short distances scaling as 1/R³. By combining this novel excitation regime with microwave-driven fields and dissipative dynamics, a stationary qutrit entangled state can be obtained with high quality, the corresponding steady-state fidelity and purity are insensitive to the variations of the dynamical parameters. Furthermore, we introduce time-dependent laser fields with periodically modulated amplitude to speed up the entanglement creation process. Numerical simulations reveal that the order of magnitude of the shortened convergence time is about 10³ in units of ω₀, and the acceleration effect appears valid in broad parametric space. The present results enrich the physics of the Rydberg antiblockade regimes and may receive more attention for the experimental investigations in dissipative dynamics of neutral atoms.

Spatially Multiplexing of Metasurface for Manipulating the Focused Trefoil and Cinquefoil Vector Light Field

The trefoil and cinquefoil vector field are of essential significance for fundamental topology properties as the Hopf link and trefoil knots in the light field. The spatially multiplexing metasurfaces were designed with two sets of periodical nanoslits arranged alternately, each had independent geometric spiral phases and metalens phases to produce and focus vortex of the corresponding circular polarized (CP) light. By arranging the orientations of the two slit sets, the two CP vortices of the desired topological charges were obtained, the superposition of the vortices were realized to generate the vector field. With the topological charges of the vortices set to one and two, and three and two, respectively, the focused trefoil and cinquefoil vector light fields were acquired. The work would be important in broadening the applications of metasurface in areas as vector beam generations and topology of light field.

Long-Distance Entanglement Purification for Quantum Communication

High-quality long-distance entanglement is essential for both quantum communication and scalable quantum networks. Entanglement purification is to distill high-quality entanglement from low-quality entanglement in a noisy environment and it plays a key role in quantum repeaters. The previous significant entanglement purification experiments require two pairs of low-quality entangled states and were demonstrated in tabletop. Here we propose and report a high-efficiency and long-distance entanglement purification using only one pair of hyperentangled state. We also demonstrate its practical application in entanglement-based quantum key distribution (QKD). One pair of polarization spatial-mode hyperentanglement was distributed over 11 km multicore fiber (noisy channel). After purification, the fidelity of polarization entanglement arises from 0.771 to 0.887 and the effective key rate in entanglement-based QKD increases from 0 to 0.332. The values of Clauser-Horne-Shimony-Holt inequality of polarization entanglement arises from 1.829 to 2.128. Moreover, by using one pair of hyperentanglement and deterministic controlled-NOT gates, the total purification efficiency can be estimated as 6.6×10^{3} times than the experiment using two pairs of entangled states with spontaneous parametric down-conversion sources. Our results offer the potential to be implemented as part of a full quantum repeater and large-scale quantum network.

Encoding scheme using quantum dots for single logical qubit information onto four-photon decoherence-free states

We designed an encoding scheme, using quantum dots (QDs), for single logical qubit information by encoding quantum information onto four-photon decoherence-free states to acquire immunity against collective decoherence. The designed scheme comprised of QDs, confined in single-sided cavities (QD-cavity systems), used for arbitrary quantum information, encoded onto four-photon decoherence-free states (logical qubits). For our scheme, which can generate the four-photon decoherence-free states, and can encode quantum information onto logical qubits, high efficiency and reliable performance of the interaction between the photons and QD-cavity systems is essential. Thus, through our analysis of the performance of QD-cavity systems under vacuum noise and sideband leakage, we demonstrate that the encoding scheme for single logical qubit information could be feasibly implemented.

Efficient Generation of High-Dimensional Entanglement through Multipath Down-Conversion

High-dimensional entanglement promises to greatly enhance the performance of quantum communication and enable quantum advantages unreachable by qubit entanglement. One of the great challenges, however, is the reliable production, distribution, and local certification of high-dimensional sources of entanglement. In this Letter, we present an optical setup capable of producing quantum states with an exceptionally high level of scalability, control, and quality that, together with novel certification techniques, achieve the highest amount of entanglement recorded so far. We showcase entanglement in 32-spatial dimensions with record fidelity to the maximally entangled state (F=0.933±0.001) and introduce measurement efficient schemes to certify entanglement of formation (E_{oF}=3.728±0.006). Combined with the existing multicore fiber technology, our results will lay a solid foundation for the construction of high-dimensional quantum networks.

Entanglement Detection beyond Measuring Fidelities

One of the most widespread methods to determine if a quantum state is entangled, or to quantify its entanglement dimensionality, is by measuring its fidelity with respect to a pure state. In this Letter, we find a large class of states whose entanglement cannot be detected in this manner; we call them unfaithful. We find that unfaithful states are ubiquitous in information theory. For small dimensions, we check numerically that most bipartite states are both entangled and unfaithful. Similarly, numerical searches in low dimensions show that most pure entangled states remain entangled but become unfaithful when a certain amount of white noise is added. We also find that faithfulness can be self-activated, i.e., there exist instances of unfaithful states whose tensor powers are faithful. To explore how the fidelity approach limits the quantification of entanglement dimensionality, we generalize the notion of an unfaithful state to that of a D unfaithful state, one that cannot be certified as D-dimensionally entangled by measuring its fidelity with respect to a pure state. For describing such states, we additionally introduce a hierarchy of semidefinite programming relaxations that fully characterizes the set of states of Schmidt rank at most D.

Fast camera spatial characterization of photonic polarization entanglement

Scalable technologies to characterize the performance of quantum devices are crucial to creating large quantum networks and quantum processing units. Chief among the resources of quantum information processing is entanglement. Here we describe the full temporal and spatial characterization of polarization-entangled photons produced by Spontaneous Parametric Down Conversions using an intensified high-speed optical camera, Tpx3Cam. This novel technique allows for precise determination of Bell inequality parameters with minimal technical overhead, and for new characterization methods for the spatial distribution of entangled quantum information. The fast-optical camera could lead to multiple applications in Quantum Information Science, opening new perspectives for the scalability of quantum experiments.

Genuine time-bin-encoded quantum key distribution over a turbulent depolarizing free-space channel

Despite its widespread use in fiber optics, encoding quantum information in photonic time-bin states is usually considered impractical for free-space quantum communication as turbulence-induced spatial distortion impedes the analysis of time-bin states at the receiver. Here, we demonstrate quantum key distribution using time-bin photonic states distorted by turbulence and depolarization during free-space transmission. Utilizing a novel analyzer apparatus, we observe stable quantum bit error ratios of 5.32 %, suitable for generating secure keys, despite significant wavefront distortions and polarization fluctuations across a 1.2 km channel. This shows the viability of time-bin quantum communication over long-distance free-space channels, which will simplify direct fiber/free-space interfaces and enable new approaches for practical free-space quantum communication over multi-mode, turbulent, or depolarizing channels.

High-speed and Large-scale Privacy Amplification Scheme for Quantum Key Distribution

State-of-art quantum key distribution (QKD) systems are performed with several GHz pulse rates, meanwhile privacy amplification (PA) with large scale inputs has to be performed to generate the final secure keys with quantified security. In this paper, we propose a fast Fourier transform (FFT) enhanced high-speed and large-scale (HiLS) PA scheme on commercial CPU platform without increasing dedicated computational devices. The long input weak secure key is divided into many blocks and the random seed for constructing Toeplitz matrix is shuffled to multiple sub-sequences respectively, then PA procedures are parallel implemented for all sub-key blocks with correlated sub-sequences, afterwards, the outcomes are merged as the final secure key. When the input scale is 128 Mb, our proposed HiLS PA scheme reaches 71.16 Mbps, 54.08 Mbps and 39.15 Mbps with the compression ratio equals to 0.125, 0.25 and 0.375 respectively, resulting achievable secure key generation rates close to the asymptotic limit. HiLS PA scheme can be applied to 10 GHz QKD systems with even larger input scales and the evaluated throughput is around 32.49 Mbps with the compression ratio equals to 0.125 and the input scale of 1 Gb, which is ten times larger than the previous works for QKD systems. Furthermore, with the limited computational resources, the achieved throughput of HiLS PA scheme is 0.44 Mbps with the compression ratio equals to 0.125, when the input scale equals up to 128 Gb. In theory, the PA of the randomness extraction in quantum random number generation (QRNG) is same as the PA procedure in QKD, and our work can also be efficiently performed in high-speed QRNG.

Photonic quantum information processing: a review

Photonic quantum technologies represent a promising platform for several applications, ranging from long-distance communications to the simulation of complex phenomena. Indeed, the advantages offered by single photons do make them the candidate of choice for carrying quantum information in a broad variety of areas with a versatile approach. Furthermore, recent technological advances are now enabling first concrete applications of photonic quantum information processing. The goal of this manuscript is to provide the reader with a comprehensive review of the state of the art in this active field, with a due balance between theoretical, experimental and technological results. When more convenient, we will present significant achievements in tables or in schematic figures, in order to convey a global perspective of the several horizons that fall under the name of photonic quantum information.

Reconfigurable vortex beam generator based on the Fourier transformation principle

A method to generate the optical vortex beam with arbitrary superposition of orbital angular momentum (OAM) on photonic chip is proposed. The components of different OAMs can be controlled by the phases of incident light based on the Fourier transformation principle. A typical device composed of nine Fourier holographic gratings is illustrated, where the OAMs of the generated optical vortex beam can be controlled on-demand from -2nd to 2nd and the working bandwidth is about 80 nm. Our work provides a feasible method to manipulate the vortex beam or detect arbitrary superposition of OAMs in the integrated photonics.

Polarization Entanglement by Time-Reversed Hong-Ou-Mandel Interference

Sources of entanglement are an enabling resource in quantum technology, and pushing the limits of generation rate and quality of entanglement is a necessary prerequisite towards practical applications. Here, we present an ultrabright source of polarization-entangled photon pairs based on time-reversed Hong-Ou-Mandel interference. By superimposing four pair-creation possibilities on a polarization beam splitter, pairs of identical photons are separated into two spatial modes without the usual requirement for wavelength distinguishability or noncollinear emission angles. Our source yields high-fidelity polarization entanglement and high pair-generation rates without any requirement for active interferometric stabilization, which makes it an ideal candidate for a variety of applications, in particular those requiring indistinguishable photons.

Postselection-Loophole-Free Bell Violation with Genuine Time-Bin Entanglement

Entanglement is an invaluable resource for fundamental tests of physics and the implementation of quantum information protocols such as device-independent secure communications. In particular, time-bin entanglement is widely exploited to reach these purposes both in free space and optical fiber propagation, due to the robustness and simplicity of its implementation. However, all existing realizations of time-bin entanglement suffer from an intrinsic postselection loophole, which undermines their usefulness. Here, we report the first experimental violation of Bell's inequality with "genuine" time-bin entanglement, free of the postselection loophole. We introduced a novel function of the interferometers at the two measurement stations, that operate as fast synchronized optical switches. This scheme allowed us to obtain a postselection-loophole-free Bell violation of more than 9 standard deviations. Since our scheme is fully implementable using standard fiber-based components and is compatible with modern integrated photonics, our results pave the way for the distribution of genuine time-bin entanglement over long distances.

Preparation of quantum information encoded on three-photon decoherence-free states via cross-Kerr nonlinearities

We present a scheme to encode quantum information (single logical qubit information) into three-photon decoherence-free states, which can conserve quantum information from collective decoherence, via nonlinearly optical gates (using cross-Kerr nonlinearities: XKNLs) and linearly optical devices. For the preparation of the decoherence-free state, the nonlinearly optical gates (multi-photon gates) consist of weak XKNLs, quantum bus (qubus) beams, and photon-number-resolving (PNR) measurement. Then, by using a linearly optical device, quantum information can be encoded on three-photon decoherence-free state prepared. Subsequently, by our analysis, we show that the nonlinearly optical gates using XKNLs, qubus beams, and PNR measurement are robust against the decoherence effect (photon loss and dephasing) in optical fibers. Consequently, our scheme can be experimentally implemented to efficiently generate three-photon decoherence-free state encoded quantum information, in practice.

Optical scheme for generating hyperentanglement having photonic qubit and time-bin via quantum dot and cross-Kerr nonlinearity

We design an optical scheme to generate hyperentanglement correlated with degrees of freedom (DOFs) via quantum dots (QDs), weak cross-Kerr nonlinearities (XKNLs), and linearly optical apparatuses (including time-bin encoders). For generating hyperentanglement having its own correlations for two DOFs (polarization and time-bin) on two photons, we employ the effects of optical nonlinearities using a QD (photon-electron), a parity gate (XKNLs), and time-bin encodings (linear optics). In our scheme, the first nonlinear multi-qubit gate utilizes the interactions between photons and an electron of QD confined in a single-sided cavity, and the parity gate (second gate) uses weak XKNLs, quantum bus, and photon-number-resolving measurement to entangle the polarizations of two photons. Finally, for efficiency in generating hyperentanglement and for the experimental implementation of this scheme, we discuss how the QD-cavity system can be performed reliably, and also discuss analysis of the immunity of the parity gate (XKNLs) against the decoherence effect.

Four-dimensional entanglement distribution over 100 km

High-dimensional quantum entanglement can enrich the functionality of quantum information processing. For example, it can enhance the channel capacity for linear optic superdense coding and decrease the error rate threshold of quantum key distribution. Long-distance distribution of a high-dimensional entanglement is essential for such advanced quantum communications over a communications network. Here, we show a long-distance distribution of a four-dimensional entanglement. We employ time-bin entanglement, which is suitable for a fibre transmission, and implement scalable measurements for the high-dimensional entanglement using cascaded Mach-Zehnder interferometers. We observe that a pair of time-bin entangled photons has more than 1 bit of secure information capacity over 100 km. Our work constitutes an important step towards secure and dense quantum communications in a large Hilbert space.

Extending Wheeler's delayed-choice experiment to space

Gedankenexperiments have consistently played a major role in the development of quantum theory. A paradigmatic example is Wheeler's delayed-choice experiment, a wave-particle duality test that cannot be fully understood using only classical concepts. We implement Wheeler's idea along a satellite-ground interferometer that extends for thousands of kilometers in space. We exploit temporal and polarization degrees of freedom of photons reflected by a fast-moving satellite equipped with retroreflecting mirrors. We observe the complementary wave- or particle-like behaviors at the ground station by choosing the measurement apparatus while the photons are propagating from the satellite to the ground. Our results confirm quantum mechanical predictions, demonstrating the need of the dual wave-particle interpretation at this unprecedented scale. Our work paves the way for novel applications of quantum mechanics in space links involving multiple photon degrees of freedom.